Frequency domain design for digital Laguerre networks

The design of digital Laguerre networks with a complex desired frequency response and the Chebyshev error criterion is investigated. This nonlinear optimization problem in the complex domain can be converted to an equivalent semi-infinite linear programming problem. Additional constraints are introduced to control the group delay error (i.e., allowing approximate rather than exact linear phase). The Laguerre network with approximately linear phase in the passband can achieve the same desired specification as the conventional FIR filters with a smaller number of coefficients, especially for narrow-band specifications.